# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.2 | Set 1

• Last Updated : 14 Jul, 2021

### Question 1. Differentiate y = sin (3x + 5) with respect to x.

Solution:

We have,

y = sin (3x + 5)

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 2. Differentiate y = tan2 x with respect to x.

Solution:

We have,

y = tan2 x

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 3. Differentiate y = tan (x + 45°) with respect to x.

Solution:

We have,

y = tan (x + 45°)

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 4. Differentiate y = sin (log x) with respect to x.

Solution:

We have,

y = sin (log x)

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 5. Differentiate y = esin √xwith respect to x.

Solution:

We have,

y = esin √x

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

### Question 6. Differentiate y = etan x with respect to x.

Solution:

We have,

y = etan x

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 7. Differentiate y = sin2 (2x + 1) with respect to x.

Solution:

We have,

y = sin2 (2x + 1)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

As sin 2A = 2 sin A cos A, we get

### Question 8. Differentiate y = log7 (2x − 3) with respect to x.

Solution:

We have,

y = log7 (2x − 3)

As , we have

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 9. Differentiate y = tan 5x° with respect to x.

Solution:

We have,

y = tan 5x°

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 10. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 11. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 12. Differentiate y = logx 3 with respect to x.

Solution:

We have,

y = logx 3

As , we get

y =

On differentiating y with respect to x we get,

On using chain rule, we have

As , we get

### Question 13. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 14. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 15. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 16. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 17. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 18. Differentiate y = (log sin x)2 with respect to x.

Solution:

We have,

y = (log sin x)2

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 19. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

### Question 20. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

### Question 21. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using product rule, we have

On using chain rule, we have

### Question 22. Differentiate y = sin(log sin x) with respect to x.

Solution:

We have,

y = sin(log sin x)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

### Question 23. Differentiate y = etan 3x with respect to x.

Solution:

We have,

y = etan 3x

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 24. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we have

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